The headline on the newspaper Nadia looks at on the 6 train reads, "The Two Faces of John LeBoutillier." LeBoutillier was a Republican congressman serving New York's 6th District. He lost the reelection and was later fined $7,000 for violating federal election laws in that campaign.
When Nadia comments that New Jersey is free to enter, but you have to pay to leave is a reference to the fact that all New York City toll roads charge only to enter, exiting the city via the any tunnel or bridge is always free.
When Nadia wonders if the hospital is performing "a Beckett Play" she is referring to Samuel Beckett's, "Waiting for Godot", a play that consists entirely of (mostly) two characters conversing while waiting for an enigmatic third person who never arrives.
While the signage suggests that Nadia is at the 77th Street Station of the 6 line, the scene was not shot at the actual station. The 77th Street Lenox Hill Hospital stop only has two tracks, whereas the one in the scene has four. The presence of an F train behind Nadia and the four tracks suggests that this may have actually been filmed at the Church Avenue subway stop.